It's possible, but again, I think it's unlikely. @FloorCandy may be on to something about a small predator reaching through the wire. If you were in north America, I might think raccoon, but since you're in the UK, perhaps a weasel?So I’ve checked and there’s no sign that anything might have got in at all.
One other thought we have had, one of the females recently has been piling up eggs in a nest & when my housemate tried to collect eggs from that area the other day the quail was trying to peck her hand. Is it possible that a female may be trying to protect her nest?
This is a close up of the injury: